After experiencing its fair share of setbacks, SpaceX has finally done it. At 3:44 a.m. EDT, the company successfully launched its Dragon capsule into low Earth orbit atop its towering Falcon 9 rocket. In doing so, it has become the first private company in history to send a spacecraft to the International Space Station.

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"Today marks the beginning of a new era in exploration; a private company has launched a spacecraft to the International Space Station that will attempt to dock there for the first time," said NASA Administrator Charles Bolden in a speech delivered at Cape Canaveral, where the Falcon 9 launch vehicle's engines rumbled to life this morning. "And while there is a lot of work ahead to successfully complete this mission, we are certainly off to good start."

The company's Dragon capsule has already passed its first two post-launch tests. Less than ten minutes after lift-off, the spacecraft successfully separated from the Falcon 9 launch vehicle. Two minutes later, the capsule successfully deployed its solar arrays.

You can experience the entire launch — from about an hour beforehand, all the way through solar deployment — in the video featured here. Lift-off occurs at 44:43, spacecraft separation at 54:10, and solar array deployment at 56:20. Excitement over the success of the launch is palpable from about 56:20 onward.

Dragon will spend the next few days coursing the International Space Station around Earth, and conducting a variety of maneuvers and systems checks to verify that it is prepared to dock with the station. If all goes well, Dragon should berth to the ISS on Friday, and have its contents transferred to the station early Saturday morning.

"The significance of this day cannot be overstated," said Bolden. "It's a great day for America. It's actually a great day for the world because there are people who thought that we had gone away, and today says, 'No, we're not going away at all.'"